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Determination of high‐order fields for multianisotropic material antiplane V‐notches and inclusions by the asymptotic expansion technique and an overdeterministic method
Author(s) -
Yao Shanlong,
Zappalorto Michele,
Cheng Changzheng,
Niu Zhongrong,
Li Jingchuan
Publication year - 2020
Publication title -
fatigue and fracture of engineering materials and structures
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.887
H-Index - 84
eISSN - 1460-2695
pISSN - 8756-758X
DOI - 10.1111/ffe.13202
Subject(s) - antiplane shear , singularity , mathematical analysis , asymptotic expansion , ordinary differential equation , eigenvalues and eigenvectors , mathematics , matrix (chemical analysis) , stress (linguistics) , asymptotic analysis , anisotropy , differential equation , geometry , finite element method , materials science , physics , structural engineering , stress intensity factor , composite material , optics , engineering , linguistics , philosophy , quantum mechanics
In this paper, the singular behavior for anisotropic multimaterial V‐notched plates is investigated under antiplane shear loading condition. Firstly, the elastic governing equations are transformed into eigen ordinary differential equations through introducing the asymptotic expansions of displacements near the notch tip. The stress singularity exponents, including the higher‐order terms, and the corresponding eigen angular functions are then obtained by solving the established equations by using the interpolating matrix method. Thus, using the combination of the results from finite element analyses and the derived asymptotic expansion, an overdeterministic method is employed to calculate the amplitudes of the coefficients in the asymptotic expansions. Finally, the stress and displacement fields in the vicinity of the notch tip, consisting of both singular terms and higher‐order terms, are determined. The effects of material properties and geometry characteristic on the singular behaviour of the notch tip are discussed in detail.